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FRBSF ECONOMIC LETTER
Number 2004-30, October 29, 2004
Inflation-Induced Valuation Errors
in the Stock Market
A recent front-page article in the Wall Street Journal
documented an increasing tendency among economists to move away from theories of efficient stock
market valuation in favor of “behavioral” models
that emphasize the role of irrational investors (see
Hilsenrath 2004). The long-run rate of return on
stocks is ultimately determined by the stream of
corporate earnings distributions (cash flows) that accrue to shareholders. In assigning prices to stocks,
efficient valuation theory says that rational investors
should discount real cash flows using real interest
rates or discount nominal cash flows using nominal
interest rates.Twenty-five years ago, Modigliani and
Cohn (1979) put forth the hypothesis that investors
may irrationally discount real cash flows using nominal interest rates—a behavioral trait that would lead
to inflation-induced valuation errors.This Economic
Letter examines some recent research that finds support for the Modigliani-Cohn hypothesis. In particular, studies show that the Standard & Poor’s (S&P)
500 stock index tends to be undervalued during
periods of high expected inflation (such as the late
1970s and early 1980s) and overvalued during periods of low expected inflation (such as the late 1990s
and early 2000s). This result implies that the long
bull market that began in 1982 can be partially attributed to the stock market’s shift from a state of undervaluation to one of overvaluation. Going forward, the
return on stocks could be influenced by a shift in the
opposite direction.
Stock as a “disguised bond”
Famed investor Warren Buffett has described a stock
as a type of “disguised bond.” A stock represents a
claim to a stream of earnings distributions, whereas a
bond represents a claim to a stream of coupon payments. Given that stocks and bonds can be viewed
as competing assets in a portfolio, investors may wish
to compare the valuations of these two asset classes
in some quantitative way. Wall Street practitioners
typically compare the earnings yield on stocks (denoted here by the E/P ratio, the inverse of the priceearnings ratio) with the nominal yield on a long-term
U.S. Treasury bond. Stocks are supposedly undervalued relative to bonds when the E/P ratio exceeds
the nominal bond yield and supposedly overvalued
relative to bonds when the E/P ratio is below the
nominal bond yield.This valuation technique is often
referred to as the “Fed model,” but it is important
to note that the Federal Reserve neither uses nor
endorses it. Many authors, including Ritter and Warr
(2002) and Asness (2003), have pointed out that the
practice of comparing a real number like the E/P
ratio to a nominal yield does not make sense.While it
would be more correct to compare the E/P ratio to
a real bond yield, that comparison still ignores the different risk characteristics of stocks versus bonds and the
reality that, over the past four decades, cash distributions to shareholders in the form of dividends have
averaged only about 50% of earnings.
Long-run yield comparison
Wall Street practitioners often argue that comparing
the E/P ratio to a nominal bond yield is justified by
the observed comovement of the two series in the
data. Figure 1 plots the E/P ratio of the S&P 500
index (based on 12-month trailing reported earnings) together with the nominal and real yields on
a long-term U.S. Treasury bond (with a maturity
near 20 years). The figure uses monthly data from
December 1945 to June 2004.The real yield is obtained by subtracting expected inflation from the
nominal yield. Expected inflation is constructed as an
exponentially weighted moving average of past (12-
Figure 1
Yield comparison: stocks vs. bonds
Sources: Ibbotson Associates (2004), www.econ.yale.edu/~shiller/data.htm,
www2.standardandpoors.com
FRBSF Economic Letter
month) CPI inflation, where the weighting scheme
is set to approximate the time-series behavior of the
one-year-ahead inflation forecast from the Survey of
Professional Forecasters.
The figure shows that the E/P ratio is more strongly
correlated with movements in the nominal yield
than with the real yield, particularly since the mid1960s.This result is a puzzle from the perspective of
efficient valuation theory. Observed movements in
the nominal yield can be largely attributed to changes
in expected inflation which, in turn, have been driven by changes in actual inflation. If investors were
rationally discounting future nominal cash flows using
nominal interest rates, they would understand that
inflation-induced changes in the nominal bond yield
are accompanied by inflation-induced changes in
the magnitude of future nominal cash flows. Indeed,
Asness (2003) shows that low-frequency movements
in the U.S. inflation rate are almost entirely passed
through to changes in the growth rate of nominal
earnings for the S&P 500 index.Thus, to a first approximation, a real valuation number like the E/P ratio
(or its inverse, the P/E ratio) should not move at all
in response to changes in the nominal bond yield.
Similar logic applies to the residential housing market;
the ratio of house prices to rents (a real valuation
number) should not be affected by inflation-induced
changes in mortgage interest rates. Nevertheless, the
data show that the ratio of house prices to rents in
the U.S. economy has been trending up since the
mid-1980s as inflation and mortgage interest rates
have been trending down.
The observation that real valuation ratios are correlated with movements in nominal interest rates lends
credence to the Modigliani-Cohn hypothesis. Investors and homebuyers appear to be adjusting their discount rates to match the prevailing nominal interest
rate. However, for some unexplained reason, they do
not simultaneously adjust their forecasts of future
nominal cash flows, i.e., earnings distributions or
imputed rents.The failure to take into account the
influence of inflation on future nominal cash flows
is an expectational error that is equivalent to discounting real cash flows using a nominal interest rate.
Changing risk perceptions
Asness (2000) shows that movements in the E/P ratio
also appear to be driven by changes in investors’ risk
perceptions. Monthly stock return volatility has declined relative to monthly bond return volatility,
regardless of whether returns are measured in nominal or real terms. If investors’ risk perceptions are
based on their own generation’s volatility experience,
then stocks will appear to have become less risky
relative to bonds over time. Following Asness, a sta-
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Number 2004-30, October 29, 2004
Figure 2
Observed vs. predicted P/E ratios
Source: Author’s calculations.
tistical model of investor behavior can be constructed
by regressing the E/P ratio on a constant term and
three nominal explanatory variables: (1) the yield on
a long-term government bond, (2) the volatility of
monthly stock returns over the preceding 20 years,
and (3) the volatility of monthly bond returns over
the preceding 20 years. It turns out that this simple
behavioral model can account for 70% of the variance in the observed E/P ratio from December 1945
to June 2004. In contrast, an otherwise identical model
that employs real explanatory variables can account
for only 26% of the variance in the observed E/P
ratio. In Figure 2, the fitted E/P ratios from both the
nominal and real models are inverted for comparison
with the observed P/E ratio of the S&P 500 index.
The nominal model does a much better job of matching the level and volatility of the observed P/E ratio.
The real model, in contrast, predicts a relatively stable P/E ratio—one that remains close to its long-run
average over much of the sample period, particularly
during the so-called “new economy” years of the late
1990s and beyond. At the end of the sample period
in June 2004, the observed P/E ratio is 20.2.The predicted P/E ratio from the nominal model is 24.1
while that from the real model is 14.8.
Inflation-induced valuation errors
The predicted P/E ratio from the real model can be
interpreted as an estimate of the rational (or fundamentals-based) P/E ratio because the model assumes
that investors discount real cash flows using real interest rates. In this case, the difference between the observed P/E ratio and the real-model prediction can
be viewed as a measure of overvaluation. Figure 3
shows that overvaluation (measured as a percent of
FRBSF Economic Letter
Figure 3
Valuation error vs. expected inflation
fundamental value) is negatively correlated with the
level of expected inflation; overvaluation tends to be
high when expected inflation is low, and vice versa.
According to the analysis, overvaluation was highest during the late 1990s and early 2000s—a period
when expected and actual inflation were quite low.
The late 1990s witnessed the emergence of the biggest bubble in history. The bubble burst in March
2000, setting off a chain of events that eventually
dragged the U.S. economy into a recession in 2001.
The recession-induced collapse in corporate earnings caused the market P/E ratio to spike above 45,
thereby exceeding the previous high that had prevailed near the bubble peak. In contrast, the high
inflation era of the late 1970s and early 1980s was
characterized by substantial undervaluation, as the
market P/E ratio languished below its long-run average for more than a decade. The results plotted in
Figure 3 reinforce those of Ritter and Warr (2002)
and Campbell and Vuolteenaho (2004), who find
strong support for the Modigliani-Cohn hypothesis
using more sophisticated empirical methods.
Conclusion
In recent years, contributors to the rapidly growing
field of behavioral finance have been refining a new
class of asset pricing models.These models are motivated by a variety of empirical and laboratory evidence
which shows that people’s decisions and forecasts
are often less than fully rational. Simple behavioral
models can account for many observed features of
real-world stock market data including: excess volatility of stock prices, time-varying volatility of returns,
long-horizon predictability of returns, bubbles dri-
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Number 2004-30, October 29, 2004
ven by optimism about the future, and market crashes
that restore attention to fundamentals (see, for example, Lansing 2004 and the references cited therein).
Twenty-five years ago, Modigliani and Cohn (1979),
put forth a behavioral model that predicted mispricing of stocks in the presence of changing inflation.
The comovement of the stock market E/P ratio
with the nominal bond yield observed since the mid1960s (when U.S. inflation started rising) is consistent
with the Modigliani-Cohn hypothesis. A regression
model that includes a constant term and three nominal variables can account for 70% of the variance
in the observed E/P ratio over the past four decades.
However, as noted by Asness (2003), the success of
this model in describing investor behavior should
not be confused with the model’s ability to forecast
what investors should really care about, namely, longrun real returns. Investors of the early 1980s probably did not anticipate the 20-year declining trend
of inflation and nominal interest rates that helped
produce above-average real returns as stocks moved
from a state of undervaluation to one of overvaluation in the manner by described by Modigliani and
Cohn (1979).Today’s investors may suffer the opposite fate if a secular trend of rising inflation and nominal interest rates causes the stock market to move
back towards a state of undervaluation.
Kevin J. Lansing
Senior Economist
References
Asness, C.S. 2003. “Fight the Fed Model.” Journal of
Portfolio Management 30(1) (Fall) pp. 11–24.
Asness, C.S. 2000.“Stocks versus Bonds: Explaining the
Equity Risk Premium.” Financial Analysts Journal
56(2) pp. 96–113.
Campbell, J.Y., and T.Vuolteenaho. 2004.“Inflation Illusion and Stock Prices.” American Economic Review,
Papers and Proceedings 94, pp. 19–23.
Hilsenrath, J.E. 2004.“Stock Characters: As Two Economists Debate Markets, the Tide Shifts.” Wall Street
Journal, October 18, p. A1.
Lansing, K.J. 2004. “Lock-in of Extrapolative Expectations in an Asset Pricing Model.” FRBSF Working
Paper 2004-06. http://www.frbsf.org/publications/
economics/papers/2004/wp04-06bk.pdf
Modigliani, F., and R.A. Cohn. 1979.“Inflation, Rational Valuation and the Market.” Financial Analysts
Journal 35, pp. 24–44.
Ritter, J.R., and R.S. Warr. 2002. “The Decline of
Inflation and the Bull Market of 1982–1999.”
Journal of Financial and Quantitative Analysis 37(1)
pp. 29–61.
Stocks, Bonds, Bills, and Inflation 2004 Yearbook. 2004.
Chicago: Ibbotson Associates.
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TITLE
Workplace Practices and the New Economy
Can International Patent Protection Help a Developing Country Grow?
Globalization:Threat or Opportunity for the U.S. Economy?
Interest Rates and Monetary Policy: Conference Summary
Policy Applications of a Global Macroeconomic Model
Banking Consolidation
Has the CRA Increased Lending for Low-Income Home Purchases?
New Keynesian Models and Their Fit to the Data
The Productivity and Jobs Connection:The Long and the Short Run of It
The Computer Evolution
Monetary and Financial Integration: Evidence from the EMU
Does a Fall in the Dollar Mean Higher U.S. Consumer Prices?
Measuring the Costs of Exchange Rate Volatility
Two Measures of Employment: How Different Are They?
City or Country:Where Do Businesses Use the Internet?
Exchange Rate Movements and the U.S. International Balance Sheet
Supervising Interest Rate Risk Management
House Prices and Fundamental Value
Gauging the Market’s Expectations about Monetary Policy
Consumer Sentiment and the Media
AUTHOR
Black/Lynch
Valderrama
Parry
Dennis/Wu
Dennis/Lopez
Kwan
Laderman
Dennis
Walsh
Valletta/MacDonald
Spiegel
Valderrama
Bergin
Wu
Forman et al.
Cavallo
Lopez
Krainer/Wei
Kwan
Doms
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